How can magnetism generate electric currents?

Magnetism can move charge, which is current.

Motional EmfEdit

Why is current induced through a piece of wire moving through a magnetic field?

Imagine the wire as a group of singular charges. As each charge moves through the field, it experiences a force, pushing it to either end of the wire. Movement of charges is the definition of current.

What is electromagnetic equilibrium?

When the force from the electric field is equal to the force from the magnetic field. The magnetic force is due to the moving charge, and the electrostatic force is due to the separation of charges, which creates a field.
FE = FB = qEf = qvB ; So at electromagnetic equilibrium, Ef = vB

What is the potential difference of that piece of wire?

V = Efd = El ; Electromagnetic equilibrium, E = vB, so V = Blv

What is (the formula of) motional emf?

Sliding a rod along conducting rails, voltage difference creates current. Can think of magnetic field as "pushing" charges, creating current.
Є = Blv, when it it just the rod creating voltage.

What force & power must be applied to the rod to create a constant velocity?

Fapp = FB; Papp/B = Fapp/Bv = (IlB)v = P = IV = I(Blv)

Faraday's Law of Electromagnetic InductionEdit

What is (the formula for) magnetic flux?

Ф = BA(sinθ). It is representative of the density of field lines which pierce the area A perpendicularly.

What is Faraday's Law of Electromagnetic Induction?

avg| = |ΔФ/Δt|

What is Lenz's Law?

The induced current will flow in the direction that opposes the change in magnetic flux that produced it.
Єavg = -ΔФ/Δt

A loop rotates in a field and then stops. How does the flow of the current change?

It flows until it stops rotating. While the loop is rotating, Єavg = -ΔФ/Δt, ΔФ = BA(Δsinθ). When it stops rotating, no more change in anything, so no more change in flux, so no more induced voltage, and no more induced current.

What is the formula for magnitude & direction of the induced emf of the moving rod?

Єavg = -ΔФ/Δt = -ΔBA/Δt = -ΔB(lx)/Δt = -Bl(Δx/Δt) = -Blv
The direction can be found with Lenz's Law. Find direction of induced current, and then calculate the voltage.

Which way do current flow if you drop a magnet North end first into a loop of wire?

We use Lenz's Law. As the North end approaches the loop, magnetic flux increases and points down. For the current to counteract the change, the induced current must create a flux pointing up. Thus the current flows counterclockwise, as RHR says that creates a magnetic field and flux pointing up.

What is Faraday's Law adapted for multiple loops?

Єavg = -N(ΔФ/Δt)